Geometric Vision

A comprehensive C++ library for computational geometry primitives and algorithms. This project provides a robust set of tools for handling geometric objects in 2D and 3D space, including vectors, points, lines, planes, and more complex structures like DCEL (Doubly Connected Edge List).

Features

The library is modularized into several namespaces, each covering specific geometric concepts:

Core Primitives

• Vector: Template-based vector class supporting 2D and 3D operations.
  • Arithmetic operations (+, -, *, scalar multiplication)
  • Dot product, Cross product (2D/3D), Scalar triple product
  • Magnitude and Normalization
• Point: 2D and 3D point representations with various sorting utilities (e.g., top-bottom-left-right, by X, by Y).
• Line: 2D and 3D line representations defined by a point and a direction vector.
• Plane: 3D plane representation defined by a normal vector and a constant, or by three points.

Geometric Operations

• Angles: Calculate angles between:
  • Two lines (2D and 3D)
  • A plane and a line
  • Two planes
• Distance: Calculate Euclidean distances:
  • Point to Line
  • Point to Plane
• Intersection: Determine intersections for:
  • Two lines (2D and 3D)
  • Plane and Line
  • Two Planes
• Geometric Utils: Helper functions for:
  • Orientation tests (2D and 3D)
  • Collinearity and Coplanarity checks
  • Triangle area calculation
  • Relative point positioning (Left, Right, Beyond, Between)

Data Structures

• DCEL: Implementation of the Doubly Connected Edge List data structure, suitable for representing planar graphs, polygons, and meshes. Includes classes for Vertex, Edge, Face, and Polygon.

Requirements

• C++ Standard: C++20
• CMake: Version 3.20 or higher
• Dependencies: GoogleTest (for running tests)

Build Instructions

To build the project, use standard CMake commands:

mkdir build
cd build
cmake ..
make

Testing

The project uses GoogleTest for unit testing. After building, you can run the tests using ctest or by executing the binary directly.

# Inside the build directory
ctest
# OR
./geometric_vision

Usage Examples

Vector Operations

#include "vector.h"

vector::vect3D v1(1.0, 0.0, 0.0);
vector::vect3D v2(0.0, 1.0, 0.0);

// Cross product
vector::vect3D cross = vector::cross_product_3D(v1, v2); // Result: (0, 0, 1)

// Dot product
double dot = vector::dot_product(v1, v2); // Result: 0.0

Intersection

#include "intersection.h"
#include "line.h"

// Define two lines in 3D
point::point3d p1(0,0,0), p2(2,2,2);
point::point3d p3(0,2,0), p4(2,0,2);
line::line3d l1(p1, p2);
line::line3d l2(p3, p4);

point::point3d result;
if (intersection::intersection(l1, l2, result)) {
    // result contains the intersection point (1, 1, 1)
}

Plane Construction

#include "plane.h"

// Define a plane using 3 points
point::point3d p1(1,0,0);
point::point3d p2(0,1,0);
point::point3d p3(0,0,1);
plane::Plane3D myPlane(p1, p2, p3);

vector::vect3D normal = myPlane.get_normal();